Interactive graphics Understanding OLS regression Normal approximation to the Binomial distribution

Interactive graphicsInteractive graphicsUnderstanding OLS regressionUnderstanding OLS regression

Normal approximation to the Normal approximation to the Binomial Binomial distribution distribution

General Stats SoftwareGeneral Stats Software

example: OLS regressionexample: OLS regressionexample: Poisson example: Poisson

regressionregression

as well as specialized softwareas well as specialized software

Specialized softwareSpecialized software

Testing:Testing:• Classical test theoryClassical test theory

–– ITEMINITEMIN• Item response theory Item response theory

– BILOG-MGBILOG-MG– PARSCALEPARSCALE– MULTILOGMULTILOG– TESTFACTTESTFACT

Specialized softwareSpecialized software

Structural equation Structural equation modeling (SEM)modeling (SEM)–

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Specialized softwareSpecialized software

Hierarchical linear Hierarchical linear modeling (HLM) modeling (HLM) –

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Open data

Run simple linear regression

Analyze Regression Linear

Enter the DV and IV

Check for confidence intervals

Age accounts for about 37.9% of the variability in Gesell score

The regression model is significant, F(1,19) = 13.202, p = .002

The regression equation:

Y’=109.874-1.127X

Age is a significant predictor, t(9)=-3.633, p=.002. As age in months at first word increases by 1 month, the Gesell score is estimated to

decrease by about 1.127 points (95% CI: -1.776, -.478)

Output

Enter the data

Fit a Poisson loglinear model:

log(Y/pop) = + 1(Fredericia) + 2(Horsens) + 3(Kolding) + 4(Age)

Click to execute

City doesn’t seem to be a significant predictor, City doesn’t seem to be a significant predictor, whereas Age does.whereas Age does.

G2 = 46.45, df = 19, p < .01

Plot of the observed vs. fitted values--obviously model not fit

Fit another Poisson model:

log(Y/pop) = +1(Fredericia) + 2(Horsens) + 3(Kolding) + 4(Age) + 5(Age)2

Both (Age) and (Age)2 are significant predictors.

Plot of the observed vs. fitted values: model fits better

Fit a third Poisson model (simpler):

log(Y/pop) = + 1(Fredericia) + 2(Age) + 3(Age)2

All three predictors are significant.

Plot of the observed vs. fitted values: much simpler model

Item Response TheoryItem Response Theory

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